A generalized direct-form delta operator-based IIR filter withminimum noise gain and sensitivity

摘要

This brief presents the derivation of an arbitrary order deltanoperator-based direct-form IIR filter with minimum roundoff noise gainnand sensitivity. It utilizes the concept of different couplingncoefficients at different branch nodes for better noise gainnsuppression. Two possible structures for realizing the inverse deltanoperator are considered and procedures for calculating the optimalnfilter coefficients are given. By means of state-space representationnand matrix manipulation, it is also shown that expressions fornsensitivity measures of different filter coefficients and theirncorresponding roundoff noise gain expressions are the same. This enablesnthe simultaneous minimization of sensitivity and noise power for thenproposed generalized filter structure